Math Field Day 2012 Short Course Event
Symbols, Formulas, Conversion Factors, Constants, and Definitions
(foot-pound-second system of units - USCS)
Symbols
a
A
cfs
d
f
g
gpm
mgd
h
hL
in
lb
n
p
psf
psi
Q
q
R
w
S
t
v or V
2
acceleration in ft/sec
2
area in ft
3
cubic feet per second, ft /sec
depth or diameter
Darcy-Weisbach friction factor
2
gravitational acceleration in ft/sec = 32.2
2
ft/sec
gallons per minute
million gallons per day
head in ft, height in ft, pressure head in ft
Lost head in ft
inch
pound
roughness factor in Manning’s formulas
2
pressure in lb/ft , wetted perimeter in ft
2
lb/ft , gage
2
lb/in , gage
volume rate of flow in cfs
volume flow rate per unit width of channel
hydraulic radius
3
unit weight in lb/ft
3
(62.4 lb/ft for water)
Slope
Time
velocity
Conversion Factors
3
7.48 gal = 1 ft
12 in = 1 ft
60 s = 1 min
2
2
144 in = 1 ft
Unit Conversions
gal 1 min
1 ft 3
gpm  ft



sec
min 60 sec 7.48 gal
3
psi  psf 
Constants
g  32.2 ft
sec 2
w  62.4 lb 3 (water)
ft
Equations of Fluid Flow
1. Equation of Continuity
2. Energy Equation (Bernoulli
Theorem)
Hydraulic Jump
2
2
p1 v1
p
v

 z1  hL  2  2  z 2
w 2g
w 2g
hp 
p
w
2b. Velocity head
hv 
v2
2g
3. Manning formula for open
channel flow (use only in
the foot-pound-second
system)
3a. Hydraulic Radius formula
(use to get R in the
Manning formula)
4. Darcy-Weisbach formula,
head loss for flow in pipes
under pressure
Math Field Day 2012
(constant flow in rectangular
channel)
Q  A1 V1  A2 V2 = constant
2a. Pressure head
2c. Static head
5a. Depths Relationship:
q2
g
 y  y2 
 y1 y 2  1

 2 
5b. Specific Energy (E):
hs  z = elevation above a reference
E  depth  velocity head
1.486 2 / 3 1 / 2
Q  AV  A(
)R S
n
R
lb 144in 2

in 2
1 ft 2
E  y V
cross sec tional area of flow
wetted perimeter
2g
5c. Loss of head = E1
2
 L  V 

hL  f  
 d  2 g 
“Respect for the rights of others is peace.” BJ
http://www.cuyamaca.edu/bfurry
2

Furry 3 /10 /12
– E2